A Company's Manufacturing Process Uses 500 Litres of Water at a Time

question 24

Essay

A company's manufacturing process uses 500 litres of water at a time. A "scrubbing" machine then removes most of a chemical pollutant before pumping the water into a nearby lake. To meet federal regulations the treated water must not contain more than 80 parts per million (ppm) of the chemical. Because there is a fine charged if regulations are not met, the company sets the machine to attain an average of 75 ppm in the treated water. The machine's output can be described by a Normal model with a standard deviation 4.2 ppm.
a. What percent of the batches of water discharged exceed the 80 ppm standard?
b. The company's lawyers insist that not more than 2% of the treated water should be over the limit. In order to achieve this, to what mean should the company set the scrubbing machine? Assume the standard deviation does not change.

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Definitions:

Merchandise On Hand

The inventory of goods that a company currently has available for sale.

Operating Expenses

The costs associated with running a company’s day-to-day operations, excluding the cost of goods sold, such as salaries, rent, and utilities.

Net Income

The amount of profit left after all expenses, taxes, and costs have been subtracted from total revenue.

Current Asset

Assets that are expected to be converted into cash, sold, or consumed within one year or the business's operating cycle, whichever is longer.